Gordon Brown leaves the House of Commons following a meeting of the parliamentary Labour party. Photograph: Leon Neal/AFP/Getty Images

A chastened Gordon Brown yesterday promised his backbench critics that he would learn from his mistakes, as he survived Labour's worst national election results since 1918 and some of the most personal attacks ever mounted on his governing style.

At a private inquest staged only hours after the party came third in the European parliamentary elections, with less than 16% of the vote, a rebel attempt to call for a secret ballot on his leadership was seen off by party loyalists.

Speaking to a packed meeting of Labour MPs and peers, Brown adopted a humble tone, saying: "Like everyone else, I have my strengths and weaknesses. I am going to play to my strengths and address my weaknesses.

"No doubt I have much to learn about a collective way of leading the party and the government. I have to learn how to be a full-time prime minister and a full-time leader of the Labour party." He said he wanted to stay leader, not for its own sake, but because he had a mission.

The Labour rebels claim to have 50 to 60 names expressing no confidence in his leadership, but after the meeting they decided not to publish the list, in essence abandoning the revolt for the moment.

But a rebel source said: "The issues which led to the parliamentary party's concerns all remain and the issues will not go away."

The rebels admitted that they had faced opposition to their revolt from MPs who saw no alternative leader coming forward, and fears that a new leader would have to stage an early election, at which Labour would be crushed.

In a long call for unity, dwelling over the party's history since the 1930s, Brown said the party had repeatedly failed when it was divided over policy, and pointed out that in all the ministerial resignation letters of the past week, there had not been a single politician who had cited policy differences inside the party.

He repeatedly promised to learn from his errors, adding "you simply cannot solve these problems through changes at the top". He insisted he was making an argument for unity and not a plea, adding that more work needed to be done to refine the party's policies on expenses, the economy and democracy.

Among more than 20 speakers, three former ministers - Charles Clarke, Fiona Mactaggart and Tom Harris - directly called for Brown to step down.

Clarke's call was listened to in silence, according to the Labour peer Lord Foulkes, but the former cabinet minister did not hold back in his criticisms, telling Brown directly: "You bear responsibility for this state of affairs that could destroy our party." He claimed Brown's "style of politics was based on dishonesty, dividing lines and bullying".

Loyalists were led by the former Labour leader Lord Kinnock who, in a lengthy address, warned: "In politics, division carries the death penalty". The former home secretary David Blunkett said the party "cannot take the bloodletting any longer. It is a case of put up or shut up".

Some leftwing rebels acknowledged that the prime minister had bought himself more time, but said their support was conditional on genuine signs that he would change his style and up his game.

But a critic of the rebels claimed that a call by Barry Sheerman, the children's select committee chairman, for a secret ballot of Labour MPs on the future of Brown's leadership "died on his lips".

A number of speakers called for the abandonment of the part-privatisation of the Royal Mail, but the prime minister made no commitments at the meeting. Government sources said he was going to defer selling a 30% equity stake in the business, but would go ahead with the legislation as early as this summer.

Earlier the environment minister Jane Kennedy quit the government, saying she could not stomach the smears organised by Downing Street against colleagues. She said the "bullying behaviour is anathema to me", and even likened it to the methods of the Trotskyist Militant Tendency.

At a a separate meeting at Westminster, another former cabinet minister, Stephen Byers, last night claimed that Brown's leadership was being questioned "not by one faction or group, but from across the party. Those who claim otherwise are in denial about the scale and extent of the concerns that exist", he said. "We need a leader who regards Labour party members as assets to be valued. A leader who sees Labour MPs as colleagues, to be worked with, and not threats to be briefed against.

"We need someone who can voice the concerns of the British people and identify with their needs. We need a leader who can win for Labour at the next general election and not take us to a humiliating defeat. Gordon Brown is not that leader."

Frank Field, the former welfare minister, also cranked up his anti-Brown rhetoric, saying: "Even I didn't think a Brown administration would be as inept as this one. The Brownites are attempting to terrorise Labour MPs into inaction. If they succeed then we deserve our fate."